Hydraulics analysis of the Heidrun offshore field

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1 Hydraulics analysis of the Heidrun offshore field P.Andreussi & E. Sangnes University of Pisa, Italy M. Bonizzi TEA Sistemi, Italy M. Nordsveen, E. Sletfjerding &, I. Berg Martiniussen Statoil ASA, Norway Abstract The present work investigates the ability of the available 1D multi-phase flow simulators MAST [1] and OLGA [2] to reproduce measured field data on the offshore Heidrun oil field located in the North Sea. The production is tied back from two subsea templates through two 5km long 10 near horizontal pipelines and two ~400 m high risers to the Heidrun TLP. Several tests were conducted at different separator pressures (32-52 bara) and inlet oil flow rates ( Sm 3 /d) by applying a gamma densitometer downstream the riser top, just upstream the separator. For the range of test conditions the reported flow regimes are wavy-stratified flow, hydrodynamic slugging and severe slugging. For the slug flow regimes the gamma densitometer traces are used to backcalculate the relevant slug characteristics, such as the slug void, the slug body and unit length, slug velocity and frequency. When slugging occurs, analysis of the data indicates that the aeration in the slug is fairly high, around 50%, indicating that the gas entrainment into the liquid slug plays an important role in determining the relevant features of the resulting slug flow regime. Detailed flow simulator analysis of the field data show that a one-dimensional description of these phenomena can lead to a fair agreement with the data provided that the adopted closure laws are appropriate for the physical problem under investigation.

2 1 Introduction Simulation of multi-phase flows in hydrocarbon transportation flow lines is typically carried out using transient one-dimensional codes. Undoubtedly the simulator which is most widely spread in the Oil & Gas industry for transient flow assurance studies is OLGA [2].The closure laws required by the one-dimensional multi-phase flow modelling have been validated against the data of the Sintef Multiphase flow laboratory [2]. For two-phase flows, six equations are globally solved: three mass conservations equations (for gas, liquid bulk and liquid droplets), two momentum equations (liquid bulk and a mixture equation for gas and liquid droplets) and a mixture energy equation. It is herein important to remark that the standard OLGA code can simulate the effect of liquid surges due for instance to terrain-induced slugging, but is not predictive on hydrodynamic slugging. This implies that transient phenomenon such as slug growth, merge or decay is not captured by the code. Nonetheless, with an add-in module (slug tracking module) these transient phenomena are taken into account by the code, although it has to be said that in order to use this module the user must prescribe the slug initiation frequency through the so-called delay constant, which is one of the most relevant slug flow output values. Recently another code, named MAST (Multiphase Analysis and Simulation of pattern Transitions) has been developed [1]. As OLGA, MAST is a transient one-dimensional multi-phase flow simulator, but instead of relying on criteria for flow regime transitions as OLGA the code is fully predictive. This implies that transition from one flow regime to another is automatically predicted by the code as result of the integration of the governing equations. Hence, when slugging occurs, information related to the slug characteristics such as slug body length, holdup, slug velocity and frequency, comes as output of the numerical simulations. The code is based on the solution of the multi-field equations, whereby each phase is solved accounting for both continuous and dispersed fields (liquid droplets and gas bubbles). Therefore MAST can solve up to four momentum equations (for sub-layers composed of liquid continuous + gas dispersed and gas continuous + liquid dispersed, and for gas and liquid dispersed fields), four mass conservation equations (total liquid and gas, liquid and gas dispersed) and a mixture energy equation. Clearly, since the code is still based on a one-dimensional formulation, closure laws are required (for the calculation of friction factors, gas entrainment and disengagement rates, droplets atomization and deposition rates) but these equations do not change depending on the flow pattern which generates in the computational node. MAST also permits the user to adopt any desired closure which is implemented in specific code libraries. Hence the user can carry out proper sensitivity studies in order to weight the effect of using different equations as closure laws in the governing fluids equations. With regard to the numerical modelling, OLGA adopts an implicit scheme for the integration over time, whereas MAST uses a fully explicit procedure for all equation besides the pressure equation which is solved in an implicit way due to stability issues. The adopted scheme for the integration of the convective terms is the first order upwind method for both codes. Since the momentum and pressure equations are strongly coupled, special care must be taken; in OLGA the pressure and velocities are solved simultaneously, while MAST adopts a typical pressure-velocity coupling that fits well with the implemented segregated solver. The computational grids employed by MAST tend to be consistently much finer than those required by OLGA. This is due to the numerical and modelling framework of the MAST code, capturing small instabilities which may grow into slugs and avoiding numerical diffusion associated with the first

3 order upwind scheme. Contrary, the slug tracking scheme in OLGA is a non-diffusive scheme for the slugs on a sub-grid of the quite coarse standard OLGA grid. In what follows the production line which will be benchmark for testing the two codes will be presented, and then the results obtained by MAST and OLGA will be illustrated and compared against the available field data. Finally, conclusions will be drawn. 2 The Heidrun off-shore production line The basis of this work is the Heidrun field measurements done by Statoil during August These measurements were performed just after production start up from two wells to investigate the multiphase flow behaviour in the pipeline, as heavy slugging had been a problem in the operations of the line. Heidrun Nordflanken is a subsea production system with two pipelines connected to the Heidrun TLP platform. The pipelines diameter is 10 inches. Under the testing procedure, two wells D-1H and D-2H were produced through one of the pipelines into the test separator. No water was detected indicating two phase flow only. The wells are at 350 meter sea depth, and the length of the pipeline is about 5 km finishing with a vertical riser about 405 metres. The profile of the pipeline is given in Figure 1. Figure 1: Profile of the pipeline For the measurements two gamma densitometers were employed to find the average density in the cross section normal to the length axis of the pipeline. The data collected from the meters are the average densities, and the liquid fraction can be found using equation (1). gas ( εliq ) ρliqεliq ρ = ρ 1 + (1) In the above equation ρ, ρ gas, ρ liq, and ε liq denote the mixture density, the gas and liquid density and the liquid volume fraction respectively. Of course this requires that the gas and liquid densities are known, and that only two-phase flow without water is present in

4 the pipeline. The meters were positioned with a distance configuration according to Figure 2. Figure 2: The locations of the two gamma meters. The gamma source was placed at one side of the pipeline and the detector on the apposite side. For calibration purposes, the pipeline was filled with oil before the tests were initiated and the meters were calibrated against this oil with sampling rates of 6Hz. There were four different tests performed at different arrival pressures (upstream the topside choke) and flow rates to investigate at what conditions heavy slugging occurs, as indicated in Table 1. Table 1: The tests performed on the Heidrun pipeline. Test Flow rate [sm3/d] Arrival Pressure [bar] GOR [sm3/sm3] Heavy slugging ,44,37, no ,45,40,35, no ,44,42,35, at 31 bar , at 37 bar For test 1 only wavy stratified flow was observed. The measurements showed small fluctuations in the average density. For test 2 the total mass flow rate increases and it was observed hydrodynamic slugging at the lower pressures (40, 35 and 32 bar). For the two highest pressures, only small variations in the mixture density were observed. Test 3 is perhaps the most interesting of all, in that three different flow patterns could be detected by the gamma metres measurements. For the highest pressure (52 bar), stratified wavy flow was the relevant flow regime. At the lower pressures of 44, 42 and 35 bar hydrodynamic slugging generated, whereas at the lowest pressure of 31 bar severe slugging was occurring. Similar results were recorded for test 4, whereby at the highest pressure of 40 bar hydrodynamic slugging was generated, and heavy slugging was observed for the lower pressure of 37 bar. Figures 3-4 show the measured average density and the pressures for all tests. Figure 3: Measured pressure and average density for Test 1 and 2 (left and right panel respectively)

5 Figure 4: Measured pressure and average density for Test 3 and 4 (left and right panel respectively). 3 Results with MAST code The numerical simulations with MAST have been conducted using uniform computational meshes based on 1000 or 4000 grid nodes. Since the overall length of the line is around 4750 m and being the internal diameter of 10 inches, this implies that with 1000 nodes the mesh spacing is around 20 pipe diameters, while for the finer mesh (that with 4000 points) the spacing is proportionally equal to 5 pipe diameters. For each test, fixed mass flow rates were imposed at the line inlet, while the arrival (outlet) pressure upstream the topside choke was adjusted depending on the operating pressure. For each test the initial grid density was of 1000 nodes and, in case slugging occurred, a finer mesh of 4000 points was adopted to investigate possible effects due to the adopted mesh. For a comprehensive description of the mathematical and modelling framework the reader is referred to [1]. During the simulations campaign, it was verified that the two most critical closures that could dramatically affect the results were undoubtedly the gasliquid interfacial friction factor and the gas entrainment rate into the front of the slug. The first closure affects the liquid film thickness, while the second is highly important in transferring gas mass from the gas bubble into the liquid slug body. As far as the adopted closures for the friction factors are concerned, while the Moody [3] correlation was used for the wall, it was verified that the best results could be obtained when the correlation by Andreussi & Persen (1987) [4] was adopted for the gas-liquid interface. Use of correlations such as that by Taitel & Dukler (1976) [5], which typically gives a lower interfacial friction factor, would more easily lead to slugging under the examined tests, since the drag acting on the liquid film would be fairly small leading to faster liquid surges. With regard to the gas entrainment rate, the correlation which allowed the best fitting with the field data was that from Manolis (1995) [6], given below. [( u u ) ] 1.87ΩρgSi SLUG l, film φe = (2) δx In the above equation Ω, ρ g, S i, u SLUG, u l,film and δx denote a correction coefficient, the gas density, the gas-liquid interfacial chord width, the slug and liquid film velocities and adopted mesh spacing respectively. During the simulation campaign, it was verified that also the correction coefficient Ω could strongly affect the prediction results; a value of around 3 was maintained for all simulations campaign.

6 Figure (5) shows the comparison between predictions and measurements for the average, maximum and minimum mixture density for the four test cases. As expected, with increasing pressures, the average mixture density increases, which is well predicted by the code. It is interesting to notice that, according to the field data, the maximum mixture density increases for decreasing pressures. This is manifestation of interfacial disturbances which grow as the gas density becomes smaller. This trend is well reproduced by MAST for tests 2, 3 and 4, while discrepancies appear for test 1. Figure 5: Comparison between predictions and measurements for average, maximum and minimum average density (test 1 top left panel, test 2 top right panel, test 3 bottom left panel, test 4 bottom right panel). Figure 6: In the left panel, MAST predicted averaged density; in the right panel, measured density (37 bar, test 1). The simulations regarding Test 1 indicate that the dominant flow regime is wavystratified flow, in agreement with the field data. Nonetheless it has to be remarked that the code predicts smaller amplitude of oscillations compared to the field data, which can be appreciated looking at Figure (6), which shows a more in depth comparison for a pressure of 37 bar.

7 The flow regime related to Test2 is recorded to be wavy-stratified for the pressures of 52 and 45 bar, while it is hydrodynamic slugging for the lower pressures; MAST instead predicts always hydrodynamic slugging, regardless of the pressure. In fact, inspection of the top right panel of Figure (5) reveals that the code consistently over predicts the measured maximum density; this is due to the more disturbed gas-liquid interface when slugging is generated. Figure (7) compares the mixture density fluctuations at the top riser location between the code predictions and the field data measurements, which clearly illustrates that larger amplitude is obtained in the predictions. Figure 7: In the left panel, MAST predicted averaged density; in the right panel, measured density (52 bar, test 2). Nonetheless, when slugging occurs, the results in terms of slug characteristics are in fair agreement with the measurements. In fact the code predicts a frequency of around one slug per minute (as the data), with a length of around 70m (~285 diameters), which is somewhat larger than the length found from the measurements (around 54m ~ 220 diameters). With regard to test 3 the code predicts hydrodynamic slugging for the pressures of 52, 44, 42 and 35 bar, while at the lowest pressure (31bar) severe slugging occurs. The only discrepancy between predictions and measurements is found for the highest pressure, when, according to the gamma meters, stratified wavy flow was generated. Figure (8) shows the comparison between predictions and measurements for the slug body length and the slug frequency. Figure 8: Comparison between predictions and measurements for slug body length and slug frequency (test 3). The code correctly predicts heavy slugging for the lowest pressure, although it has to be said that the size of the slugs is much shorter than that recorded by the gamma meters (around the riser length according to MAST, 1.3 km according to the field data). Consequently the frequency of the severe slugging cycle is lower in MAST than in the field because of mass conservation considerations (4.5 minutes against 17). The riser

8 base pressure and the top side riser mixture density fluctuations as predicted by the code are shown in Figure 9, from which the typical periodicity of the riser slug phenomenon can be appreciated. The arising question was to check if the code was capable to sustain a severe slugging cycle with the period and a slug length given by the measurements. A new simulation was therefore run with artificial inlet boundary conditions corresponding to slug characteristics given by the field data (frequency 1/17 minutes and slug length around 1.3 km). The interesting result was that at the top riser the severe slugging cycle was maintained equivalent to what was feeding into the pipe inlet. Figure (10) shows predicted (with the slugs artificially fed into the pipe inlet) and measured mixture density and pressure fluctuations at the riser top position. Figure 9: Predictions of the top side riser mixture density (left panel) and riser base pressure fluctuations (right panel). Figure 10: Predictions (left panel) and measurements (right panel) of the top side riser mixture density and pressure fluctuations. The fact that the code is capable to predict a riser slug cycle with a period similar to the field data suggests the fact that somehow transient phenomena, such as hydrodynamic slug flow initiation and slugs merging, potentially occurring upstream the riser base are not captured (even a mesh of nodes -1 diameter mesh spacing - was used but no hydrodynamic slugging occurred before the riser). The case with steady inlet boundary conditions was further analysed with MAST using different closure laws; it was verified that a riser slug cycle more similar to what was recorded by the field data could be obtained by switching to the Spedding & Hand [7] correlation for the liquid-wall friction factor and increasing the speed (the coefficient Ω in equation (2) was set to 12) of gas entrainment rate into the slug front.

9 Figure 11: Comparison between results from MAST and field data for mixture density (left panel) and pressure fluctuations at the riser top location. Comparison between code predictions and field data for mixture density and pressure fluctuations at the riser top location upstream the choke valve is illustrated in Figure (11). The correlation for the liquid-wall friction factor based on the Spedding & Hand correlation [7] leads to a higher wall shear stress compared to the equation of Moody (for a turbulent flow regime, the friction factor is roughly 20% higher) which allows the formation of hydrodynamics slugs in the portion of the branch before the riser starts. The hydrodynamic slugs arriving at the riser base would then merge with the liquid falling backwards along the riser pipe wall (dynamic process captured in Figure 12): this is the process, according to MAST, which can lead to the formation of slugs abnormally long, provided that all the gas in the riser is entrained by the fast moving liquid slug front. Figure 12: Predictions of mixture (liquid continuous + gas bubbles) holdup profiles along the line according to MAST (time difference between left and right panel is 30 seconds). This phenomenon is forced to occur by increasing the magnitude of the gas entrainment rate which, probably, indicates that the correlation used for the standard runs is not the most appropriate under the present investigation. For Test 4 the predictions show very similar trends compared to the field data; in particular for the higher pressure of 40 bar the resulting flow regime is predicted to be hydrodynamic slugging, with relatively short (slug body length around 100 m) slugs exiting the line, in good agreement with the data (slug size 73 m). A decrease in pressure changes quite significantly the overall picture, whereby severe slugging instead occurs. Figure (13) shows a comparison, for the pressure of 37 bar, between code predictions and measurements. It is interesting to notice that the maximum predicted slug size is around 500 m, slightly higher than the riser length. The measurements instead indicate a slug size which is around three times the predicted value.

10 Figure 13: In the left panel, MAST predicted averaged density; in the right panel, measured density. Pressure set at 37 bara, test 4. This suggests that, similarly perhaps to what happens in test 3, the code may fail in predicting the correct flow pattern in the portion of the branch before the riser keeping the unified set of closure laws selected for all tests. In fact, changing the closure laws, as it was done for test 3, might have probably improved the code predictions for the severe slugging case. When heavy slugging is generated, the predicted slug formation mechanism is based on the merging of short slugs in the riser column, eventually leading to bubbly flow dominating the riser. It is herein interesting to show the average slug void as the slugs travel along the riser for different gas entrainment correlations, as illustrated in Figure (14). Figure 14: Predictions of the average slug void for different locations along the riser using two different correlations for the gas entrainment rate at the front of the slug (test 4, pressure 37 bara). One can notice that the correlation by Manolis leads to slugs which are much more aerated compared to those generated with the Gregory et al. [8] correlation, this being due, as inspection of equation (2) reveals, to the term related to the relative velocity between the slug velocity and the velocity of the liquid film, which can be negative in vertical upwards pipes (liquid back-flow), leading to a magnified entrainment rate. The averaged slug void is found to be around 55%, which is very close to the measured value (51%). The dynamics of the gas bubble entrainment based on correlations which do not account for this relative difference (such as that of Gregory at al. [8]) would be different, leading to an overall diminished aeration effect. This has of course a big impact on the

11 results, since the higher the gas bubbles entrainment rate, the higher the gas depletion from the gas bubble travelling ahead the liquid slug which consequently leads to longer slugs in the vertical riser. Table-2: Flow regimes upstream top side choke Pressur e [bar] 3000 Sm 3 /d GOR = 110 Sm 3 /Sm Sm 3 /d GOR = 109 Sm 3 /Sm Sm 3 /d 4700 Sm 3 /d GOR = 111 Sm 3 /Sm 3 GOR = 127 Sm 3 /Sm 3 Data MAST Data MAST Data MAST Data MAST 31 Terrain Slug Terrain Slug 32 Wavy Wavy stratified stratified Slug Slug 35 Slug Slug Slug Slug 37 Wavy Wavy Terrain Terrain stratified stratified Slug Slug 40 Slug Slug Slug Slug 42 Slug Slug 44 Wavy Wavy stratified stratified Slug Slug Wavy stratified Wavy stratified Wavy stratified Wavy stratified Slug Slug Wavy stratified Slug 4 Results with OLGA code Since OLGA is the most widely spread simulator for transient flow assurance studies it was interesting to also compare OLGA predictions with the Heidrun data. In the OLGA model the ~5 km long pipeline is divided into pipes with lengths of about 100 m. Each pipe is again sub-divided into sections with maximum length of 5 m. This gives a discretization similar to the MAST 1000 node case. A grid sensitivity was done by also applying section lengths of about 40 m. The topside choke and the separator volume modelled as a 100 m long pipe were included in the OLGA model. Without this enhancement no terrain slugging could be observed. 4.1 Steady state results First a screening of the flow regime before the top side choke was done. The steady state model in OLGA predicted hydrodynamic slugging for all cases in Table-2. The wavy stratified flow regime seen for all pressure level for the lowest rate and for higher pressure levels at higher rates was not depicted by OLGA. The steady state model cannot predict terrains slugging and a further investigation of terrain slugging predictions is done in next section by invoking the slug tracking model in OLGA. Three cases as shown in Table-3 were chosen for further comparisons. Table-3 Oil rate [Sm3/d] Pressure upstream choke[bar] Flow regime Stratified wavy Stratified wavy Terrain slugging

12 The topside choke CV (valve sizing coefficient) was set to 250 gal/min/psi 1/2 to match the measured pressure drop across the choke at the given opening. The chosen CV fits quite well for the first two cases at 3000 and 3800 Sm 3 /d, but for the last case at 4700 Sm 3 /d the pressure drop across the choke is too high. A CV of 300 gave a better prediction of the pressure drop across the choke at 4700 Sm 3 /d, but resulted in a too low pressure drop for the other two cases. Total pressure drop from template to downstream choke and pressure drop over choke are presented in Table-4. Total pressure drop is very well predicted for the 3800 Sm3/d case while for the 4700 Sm3/d case the pressure drop is overpredicted by ~12%. Table-4 Oil rate [Sm 3 /d] Pressure upstream choke [bar] Pressure drop over choke [bar] Pressure drop total [bar] Flow regime Meas. Meas. Pred. Meas. Pred. Meas. Pred Stratified Slug wavy Stratified Slug wavy Terrain slugging Slug 4.2 Slug tracking results In the slug tracking model in OLGA slugs are initiated at sections boundaries when the minimum slip criterion indicates slug flow, provided that the time since the previous slug initiated at that boundary is larger than a user specified limit. This limit is specified as the delay constant DC which relates the time between two consecutive slug initiations on any given boundary by: t = DC x D/U, where D is the pipe diameter [m] and U is the average liquid velocity [m/s]. The delay constant is by default 150 in OLGA. Experiences have shown that the delay constant has a large influence on the length and frequency of the slugs. This is unfortunate since this is a parameter given by the user, and to some degree the slug tracking model is thus not a predictive tool. In Table 5 average pressure, pressure variations and slugging period upstream the choke are presented for different delay constants for the terrain slugging case (4700 Sm 3 /d). It is seen that with DC = the measured slugging frequency of 17 min is reproduced. In Figure 15 measured and predicted pressure and density upstream the topside choke are compared. Table-5 Delay constant Average pressure upstream choke [bar] Pressure variations / P [bar] Steady state (3) (8) (12) (20) (1) 0.5 Slug period [min]

13 meas OLGA (CV=250, DC=10000) Density [kg/m3] Time [min] Figure 15: Oil rate 4700 Sm3/d. Simulated and measured (a) pressure and (b) density upstream choke. The effect of the gridding was checked by also running the slug tracking simulations with a much coarser grid (section lengths ~40 m). This model also gave terrain slugging with DC=10000, but the period was slightly shorter (14 min). For the present conditions DC = corresponds roughly to 5 min delay between each slug initiated. This seems to be a quite long time and we had some concerns about if this could force terrain slugging. We therefore also run the two other cases in Table-3 (oil rate 3000 and 3800 Sm 3 /d) with the slug tracking model applying DC = And indeed we also obtained terrain slugging for these cases with slug frequency 5-20 min. This is obviously highly unsatisfactory since these cases were reported to be stratified wavy. 5 Conclusions Predictions with the one dimensional transient multiphase codes MAST and OLGA have been compared with field data measurements of the Heidrun field in the North Sea. The field data campaign was initiated to investigate the multiphase flow behaviour, as heavy slugging had been a problem in the operations of the line. Two gamma densitometers were applied topside to measure the slugging behaviour. In addition pressure and temperature measurements were recorded. Four tests were conducted for varying pressures and flowrates. Stratified wavy, hydrodynamic slugging and terrain slugging were observed. The MAST predictions agree fairly well with the field data as far as the resulting flow regimes and (when it generates) the hydrodynamic slugging characteristics are concerned. While at the lowest flow rates (test 1) the flow pattern is correctly predicted (stratified-wavy), the amplitude of oscillations at the gas-liquid interface is smaller compared to the gamma densitometer signals. This may indicate that the closure for the wall and/or interfacial shear stresses is not completely satisfactorily, which could also be the reason why, at the highest pressures for Test 2 and Test 3, instead of stratified-wavy

14 flow, hydrodynamic slugging occurs. Somehow an insufficient interfacial shear is predicted, and instabilities are deemed to grow at the interface, according to the code with the adopted set of closure laws, eventually leading to slug formation. The most interesting finding is that for the tests at the highest flow rates (3 and 4) and at the lowest pressure (31 and 37 bar respectively), severe slugging is correctly predicted to generate, but with a period which is far from that recorded by the gamma densitometer (period of around 4.5 and 17 minutes for predictions and measurements respectively). This reflects in shorter slugs forming during the cycle, with an average size roughly corresponding to the riser length (~400m), while from the measurements much longer slugs (around 1.3km) are expected to form. It is only when slugs with the measured characteristics are artificially fed into the pipe inlet or when both the closure for the liquid-wall friction factor and the speed of gas entrainment rate are substantially modified that severe slugging with a large period (~17min) is predicted to occur. An enhanced liquid-wall shear stress would lead to thicker liquid films and consequently would favour slug formation, while a higher speed of gas entrainment rate would make the liquid slugs eat up more gas from the bubble moving ahead the slug. One may therefore speculate that relevant phenomena, such as hydrodynamic slug growth (obtained from an enhance liquid wall shear stress) and merging (due to the higher speed of gas entrainment rate) which may explain the formation of such long slugs, occurring prior to the riser base are not captured by the code with the adopted unified set of closure laws which though gave, on average, the best results for all cases. Standard OLGA predicted hydrodynamic slug flow before the topside choke for all 16 cases investigated. In the field measurements only 7 of these cases were reported to be hydrodynamic slugging, 7 cases were reported to be stratified wavy and 2 cases were terrain slugging. Results for one of the terrain slugging cases and two of the stratified wavy cases are presented in more detail. It is seen that the OLGA predictions showed quite good agreement with the data regarding average pressure drop even though the flow regime at the top of the riser was not correctly predicted. For the terrain slugging case the slug tracking model in OLGA were invoked, and by choosing a quite large delay constant (DC= 10000) terrain slugging with the correct frequency was predicted. This was quite encouraging, however, this model with DC=10000 also predicted terrain slugging for the two stratified wavy flow cases. With a large DC the initiation frequency of slugs is low allowing more liquid to accumulate in the line between each slug. Each slug will then scoop up more liquid and unrealistic long slugs may be generated. One may speculate that in reality more frequent slugs are generated (DC << 10000), and that under certain conditions these slugs develop/merge into long slugs and that this process is not captured by OLGA for the present terrain slugging cases. Nomenclature ρ density (kg/m 3 ) ε volume fraction (-) Ω multiplier of gas entrainment rate (-) S chord length (m) u phase velocity (m/s) δx mesh spacing (m) DC delay constant (-)

15 D pipe diameter (m) U liquid velocity (m/s) t slug period (s) Subscripts film gas i liq SLUG in liquid film gas phase inerfacial liquid in the slug REFERENCES [1] Bonizzi M., Andreussi P., Banerjee S Flow regime independent, high resolution, multi-field modelling of near horizontal gas-liquid flows in pipelines Int. J. Multiphase Flow, Vol. 35, pp [2] Bendiksen K., Malnes D., Moe R. & Nuland S The dynamic two-fluid model OLGA: theory and application SPE paper 19451, pp [3] Hall N.A Thermodynamics of fluid flow. Longmans, Green and Co. [4] Andreussi P. & Persen L.N Stratified gas-liquid flow downwardly inclined pipes Int. J. Multiphase Flow 13, [5] Taitel Y. & Dukler A.E A model for predicting flow regime transitions in horizontal and nearly horizontal gas-liquid flow J. AIChE 22, [6] Manolis I.G High Pressure Gas-Liquid Slug Flow. PhD Thesis, Chem. Eng. Dept., Imperial College London, London, UK. [7] Spedding P.L. & Hand N.P Prediction in stratified gas-liquid co-current flow in horizontal pipelines. Int. J. Heat Mass Transfer 40, [8] Gregory G.A., Nicholson M.K. & Aziz K Correlation of the liquid volume fraction in the slug for horizontal gas-liquid slug flow Int. J. Multiphase Flow 4,

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